on value maximization and alternative objectives of the firm

THE JOURNAL OF FINANCE • VOL. XXXII, NO. 2 • MAY 1977

ON VALUE MAXIMIZATION AND ALTERNATIVE OBJECTIVESOF THE FIRM

S. J. GROSSMAN AND J. E. STIGLITZ*

THE RECENT LITERATURE on firm behavior has been characterized by two contrast-ing strands of analysis: on the one hand, there is the literature attempting to extendthe conventional maxims of profit maximization of competitive firms from thefamiliar static models to dynamic contexts and into situations of uncertainty. Theseanalyses argue that firms should maximize their stock market value and explore theimplications of this for firm behavior. On the other hand, there is the vast andgrowing "managerial" literature, in which other objectives, such as "satisficing,""sales maximizing," and "maximization of the manager's utility functions" arepostulated. The second group of analyses criticize the first as being unrealistic,while the first argues that it provides the best "first approximation" to firmbehavior: if firms did not maximize their stock market value, or deviated far fromvalue maximization, someone would attempt to take them over, change the courseof action of the firm, and make a pure capital gain. This paper presents a unifiedframework for analyzing firm behavior which can be used to reconcile thesedivergent views.

We begin our analysis by taking seriously several aspects of modern corporationswhich are usually ignored: there exist shareholders' meetings, the right to vote atthese shareholders' meetings often has market value (market prices for voting andnon-voting shares often differ); disagreements occasionally arise at these meetings;takeover bids are not uncommon; and takeovers are often disputed. The moderncorporation is an economic institution in which there is always a potential political(i.e. voting) aspect. Thus, we model the firm as if the action it takes weredetermined by a majority vote of its shareholders. In deciding what action to votefor, shareholders must have some expectations of the consequences of alternativeactions; in particular, we consider a small firm, so that it is not unreasonable forthe individual to assume that the actions and values of all other firms will beunaffected. Thus we take the conventional Nash-non-cooperative view of marketequilibrium. On the other hand, the action of the firm may have an effect on themarket value of the firm in question, and it may lead individuals to decide toreallocate their portfolios.' We postpone until later a more detailed discussion ofwhat a market equilibrium would look like in this context; but the simplest case toanalyze is that where all individuals agree on what action the firm ought to take. Insome sense, when that is the case, the shareholders' meeting is redundant.

Section 1 of this paper gives an introduction to our result that in many cases

• Stanford University. This work was supported in part by National Science Foundation GrantsSOC74-22382, SOC74-11446-A01 and SOC76-18771. The authors are also indebted to the Dean WitterFoundation and IBM. We are very grateful to Oliver Hart for helpful comments.

1. For an earlier discussion of the voting-shareholders' model of the corporation, see Stiglitz [1970].

389

390 The Journal of Finance

where a stock is traded, it seems clear that there will not be stockholder unanimity.Section 2 sets up a formal model. Sections 3 and 4 critically survey the results onunanimity in the context of a multiperiod model. Section 5 shows how unanimitytheory can be used to prove and analyze the Modigliani-Miller theorem. Sections 6and 7 discuss the value of value maximization, and some paradoxes involved intake-over bids.

1. INTRODUCTION TO SHAREHOLDER UNANIMITY ,

In the conventional static models the desirability of profit maximization is obvious;there are prices for all goods and factors. The firm's "value" is simply the value ofoutput minus the value of inputs. All prices are known and the technology isknown, so there is unanimity about what course of action leads to value maximiza-tion. Value maximization is desired by every individual because an increase in themarket value of the firm simply moves the individual's budget constraint outward(in parallel, since prices are assumed to remain unchanged).

This result extends in a straightforward—and uninteresting—way to dynamicsituations with uncertainty when there is a complete set of future and contingentclaim (Arrow-Debreu) securities markets. Much of the recent literature oncorporate firm behavior can be thought of as an attempt to extend these results onunanimity to situations where there is not a complete set of markets. It has beenshown that unanimity obtains if there is no trade and if any production plan of thefirm can be written as a linear combination of production plans of other firms; i.e.there is what has come to be called spanning.

The major argument of the paper is: (i) in any interesting market there will betrade, and then spanning does not imply unanimity; in particular, we examine twosituations where trade is likely to be continuously generated; in one, trade isgenerated by the arrival of new information; it is obvious that differential informa-tion may give rise to trade, but even if the new information is obtained byeveryone, if individual tastes (attitudes towards risk) differ, the equilibrium port-folios will change in response to the new information. In the other, trade isgenerated by life cycle considerations: every period, there are individuals whoretire and who sell their shares to new individuals who hold the shares as savingsfor retirement; (ii) if the financial decisions of the firms are also taken intoaccount, spanning requires essentially a full set of markets and thus does notconstitute any weakening of the classical result, and (iii) if in addition to spanningfirms are assumed to behave as perfect competitors in the composite commoditieswhich form a basis for the spanned space, then there is unanimity. We call thisassumption "competitivity." However, the assumption of both spanning and com-petitivity lead to the very strong result that firms desire to maximize the net marketvalue of their shares. Though this may sound like a satisfactory theory it isempirically false and leaves unexplained the numerous phenomena referred to inthe introduction. In the concluding remarks we refer to empirical evidence for aparticular class of firms where there is unambigous evidence against the hypothesisof value maximization.

On Value Maximization and Alternative Objectives of the Firm 391

2. A SIMPLE MODEL: THE MULTIPERIOD MODEL WITHOUT DEBT

The economy extends for three periods: 0, 1 and 2. The state of the world, w iscomposed of a signal t, which is known in period 1 and a final state i which isknown in period 2; u = {t,s). There is a single commodity which is available in eachperiod and which is used for consumption and investment in period 0, and forconsumption only in both periods 1 and 2.

In period 0 there are markets for the single current commodity and also forshares in firms. It is assumed that no contingent commodity contracts can be made.In period 1 there are markets for the single current commodity and also for sharesin the firms. Consumers also get the signal / which changes their beliefs about .rbefore trading in period 1. In period 2 consumers are allocated output according tothe shares held in firms at the end of period 1.

Let there be / consumers, J firms,. T signals and S final states, indexed byi = \,...,I,j= \,...,J, t= l , . . . , r , s= \,...,S, respectively. Sometimes /, / , T and Swill be referred to as the set of consumers, firms, signals and final states.

Consumers

We will represent consumer i's consumption plan by a vector Xi = {x°,xl,xf)g^|+7-+7-s^ where x°ER^ is consumption in period 0 and xÊR^ is consump-tion when there is signal t in period 1, and xf{u) = xf{t,s)GR^ is consumption inperiod 2 when {t,s) was realized. Consumer /' is assumed to have a utility functionUl defined on ^|'^^+^'^. We will assume that (/, is strictly quasi concave andcontinuously differentiable on the interior of its domain, and 9( / , /3x 'ôo as x'^0f o r / = 0 , 1 .

Firms

Firmy's production possibilities are represented by a production set Y cR^'^'KIf y:e YJ we writeyj = {yj,yf) whereyfeR^ is the input in period 0 and yf{s)eRîs the output in period 2, state s. Note that inputs appear as non-negative numbers.We will assume that Y, is convex, closed and contains the origin. Further if y e Yand 7° = 0, then 7 / = 0.

It is assumed that consumer / has initial endowments x°G/? + ,3c/G/?+ of thecommodity in periods 0 and 1 respectively. He also has initial shareholdings O^j > 0in firm y where 2 / % = J for each y. For notatjonal simplicity we ignore endow-ments in period 2. Let A'°=2,Jc°, and assume X°>Q.

Equilibrium for Fixed Production Plans

Let 7 be given for each y'= l, . . . ,y. The /th consumer maximizes Uj{xf,xl,xf)with respect to {9jj,e,j{t),Xi), j=\,...,J, t = l,...,T subject to: the individual'ssecond period budget constraint,

the individual's first period budget constraint,

^,' (0 + S PjiOOijit) < 2 Pj{t)9ij+x! (t) (2)J j


(consumption plus the value of shareholdings at the end of the period (after trade)must be less than or equal to the value of shareholdings at the beginning of theperiod (before trade) plus the endowment); and the individual's 0th period budgetconstraint;

J j

where x}{s,t) is the (5,0th component of xf\ 9ij{t) is the desired holdings of firmy,in period 1 if Ms the information signal; x/(0 is the tth component of xj. pj{t) isthe price of firmy' in period 1, signal t. pj is the price of firmy' in period 0. ,y are thedesired holdings of firm j in period 0. In (3) we have assumed that inputs, yJ, arefinanced by the issuance of equity alone.

With no constraint against short sales (i.e. we don't require 9ij or 9ij{t) to benon-negative) necessary and sufficient conditions for solution to the maximumproblem are that there exist multipliers (A°,A,') such that XfGR^ and XjeRl suchthat

^^U. = Xf^ V,[/,. = A/ (4)

^2i^ryJ^KPj{^)' j=\,...,J, t=\,...,T, (6)

where VQf/, = 9[/,(x,)/8A:°, and V2,t/, = [9(/,(^,)/9x/(/,5)]^=i, and A,, is the tthcomponent of A,'.

Equation (4) provides the interpretation of the Lagrange multipliers \° and A/ asthe marginal utility of consumption between the 0th and 1st periods. The interpre-tation of (5) is perhaps clearer if we rewrite it as: />; = 2 / ( ^ 2 / ^ / / ^ ^i)'yj' ^^^ priceat date 0 equals the weighted average of the returns at date 2, with weights equal tothe marginal rate of substitution between goods at date 0 and date 1—signal t.

Equation (6) has the interpretation that the price (value) of a share in state t isequal to the marginal utility generated by buying an extra share of the firm,normalized by the marginal utility of income in state t.

A competitive exchange equilibrium for the economy, relative to the productionplans {yj) is then a collection (x,), {9ij), {9y{t)), {pj) and {pj{t)) such that (4)-(6)hold for each consumer and the commodity market at time 0 and 1 and the sharemarkets at time 0 and 1 all clear:

2 • /°+ 2 yj'-^^' 2 9ij= 1, 2 9ij{t)= 1, (7)' j • •

and yx!(t)=yxj(t

In the above economy, firms fix their inputs in period 0 and output is realized inperiod 2. In period 1 consumers get new information about the distribution of firm


output in period 2, so they have the opportunity to recontract away from theirperiod zero holdings of firm shares. In period 2, state s, each consumer gets theoutput that corresponds to his share of the firms he owns.

In the above definition of equilibrium we took as exogenously given the produc-tion plans of all firms. We now exposit some methods of determining productionplans as well as exchange equilibrium. It is useful to parameterize the firm's choiceof production plan; we letyj{pj)=yj, and assume a small change in pj correspondsto a small change in y,.^

The crucial part of an analysis involves examining how the stockholders of firmy'feel about a small change from pj to Pj + dpj. To see this we totally differentiate aconsumer's utility function with respect to p . That is, we define

^^^_^^ t / , (x , ) subject to (l)-(3).

By direct calculation

dyf dyf

In deriving equation (8) we have used equations (4)-(6) and the assumption:

dpJt) dvi, dp^- 5 ^ = :7^ = -P=0 for k=^J,\fteT. (9)

dp dp dp ^ ^ 'That is, when theyth firm changes its production decision no change is assumed tooccur in all other firms' production decisions and prices. (Here we are alreadymaking assumptions about the degree of competition among firms or, implicitlyimposing a Nash equilibrium notion on firm behavior.) If (8) has the same sign forall individuals, there is unanimity with respect to different individual evaluations ofalternative production plans. The question is when will (8) have the same sign forall individuals. It is our objective to show that the assumption of "spanning," whichis made to get unanimity in a two period context, is not sufficient in a three periodcontext. We will show that in addition to spanning the stronger assumption ofcompetitivity (to be defined below) is a sufficient condition for unanimity in a twoperiod context (i.e. one trading period).

3. UNANIMITY WITH ONLY ONE TRADING PERIOD

Suppose we close the market for shares in period 1, or that with the market open alltraders decide not to trade. In this case the firm makes its decision in period 0 andin period 2 consumers get their period 0 shares of the firm's period 2 output. That

2. We will assume that mapping yj can be found such that the exchange equilibrium prices aredifferentiable functions of pj.


is 9ij^ = 9j^{t) for all t, so equation (8) can be written as

rf(/; \ , . , dpj _ dyf(10)

The first term on the right hand side of (10) represents a wealth (i.e. a capitalgains) effect, while the second term represents a consumption effect (i.e. the changein utility due to a change in the composition of date 2 consumption).

The first term makes clear that capital gains are only important to the extent thatthe individual is a seller of the security, i.e. his initial endowment ^ exceeds hisplanned holdings of shares at the end of the period. (The term 9jj{dy°/ dpj) comesfrom the particular specification of how in effect an additional investment isfinanced; i.e. from compulsory payments from the original shareholders.)

The distinction between the consumption and capital gains effects is very clear ina different context: suppose there were a single producer of automobiles, andbecause of technological considerations, all automobiles had to be either blue orpink. Suppose, too, that more people preferred blue cars, so that the value of thefirm would be maximized by producing blue cars. But if a shareholder alsoconsumes cars, and knows that the production decision of the firm is going toaffect his "consumption set"—i.e. if the firm produces blue cars, he cannotpurchase a pink car, then a shareholder with a strong preference for pink cars, mayvote for producing pink cars, even when there is considerable loss in market valueas a result. In the context of the stock market, the point is that whenever there isnot a full set of contingent claims markets, there is always the possibility that theslope of the budget constraint is altered, not in the dramatic way of the previousexample (where the implicit relative price of the two kinds of cars, pink and blue, isaltered from infinity to zero) but still altered in an important way.

Thus, the search for conditions for unanimity breaks down into looking forconditions under which (a) there is unanimity about the sign of the consumptioneffect, (b) there is unanimity about the sign of the wealth effect, and (c) there isunanimity about the relative importance of the two.

Assume that there was a complete set of securities; then 2/'^2/^/~\°9(-^) whereq{s) is the market price for income in state s. Using (10) and (4)--(6) we obtain

Note that now the consumption effect is the same for all individuals. Moreover, inthat situation

The change in the market value is simply the value—at market prices—of thechange in inputs and outputs. The fly term then cancels, and we obtain dU^/dpj= \%j[{dpj/dpj)-{dy°/dpj)], the change in the net market value. This is the


standard result. Note, however, that there were two distinct stages in the analysis.The first involved obtaining agreement on the consumption effect, the secondinvolved relating the magnitude of the consumption effect to the capital gain effect.Thus, if there were taxes, leading to a discrepancy between consumer and producerprices, i.e. so that equation (12) did not obtain, then unanimity about the consump-tion effect would not imply overall unanimity.

It is obviously not necessary to have a complete set of securities to obtainunanimity on the consumption effect. Stiglitz [1970] noted two conditions underwhich unanimity on the consumption effect obtained: (a) if there is multiplicativeuncertainty, so that (with suitable parameterization) dyj/dpj=yj, we obtaindirectly from (4) and (6) the result that 9ij^,V^,Ui{dyj/dpj) = 9i^^2t^,-yj = \f9ijPjso the sign of the consumption effect is independent of /, for all shareholders offirm J, and (b) in the mean variance model (either a quadratic utility function orjointly normally distributed random variables), he also showed that the sign of theconsumption effect is independent of /'.

Ekern-Wilson [1974] and Leland [1974] have generalized the technological condi-tions under which stockholders are unanimous with respect to the sign of theconsumption effect. Ekern-Wilson assume that any feasible change in a firm'soutput plan can be written as a linear combination of all firms' current outputplans; with {/?}j^, given, they assume that there exist real numbers a ^ such that

dyj J^ = 2 oîkyl (13)

If (13) holds for {/,}y=i we say there is spanning at [yjYj^y Substituting toevaluate the consumption effect in (10), using (5) and (6) yields

dyj«//2 V2,f/,^ = ^y2 V2,V,âj0,l = \fe,jâj,p,, (14)

the sign of which is independent of / for all shareholders of firmy. Informally, ifany output of the firm is a linear combination of the outputs of other firms then alltraders must agree on the consumption effect of an output change, becauseconsumption opportunities are unchanged.

Consumption unanimity, as we have emphasized, does not imply overall unanim-ity for there must be unanimity about the relative importance of the consumptioneffect and the capital gains effect. It turns out that to obtain the latter, only threegeneral sets of conditions have been derived: (a) there is no capital gains effect, (b)there is no consumption effect, and (c) in addition to spanning we make theassumption (to be given formally below) of competitivity.

To see conditions under which (a) or (b) obtain Stiglitz [1970] suggested that it isuseful to isolate two phases in a corporation's life cycle; in the early phase, a smallgroup of investors own the firm and want to raise capital to expand, and eachmember wants to diversify his personal wealth into other securities. In this earlyphase, the initial stockholders have very large Sjj (initial holdings) relative to 9jj(desired holdings). Thus, assuming that fl,y?wO we can write (10) as dU^/d


^Xf9jj[{dpj/dpj)-{dyJ'/dpj)], i.e. the consumption effect is negligible; clearly in thiscase, all stockholders desire the firm to maximize net market value.

In the mature steady state stage of a firm's existence, stockholders simply holdtheir portfolio shares every period, e.g. in a world with no new information or othershocks hitting the market, a steady state-* means that 9jj = ^y, so the capital gainseffect drops out, and we obtain only the consumption effect (where, obviously, ifthere is additional investment in the 0th period, we must take the cost of that intoaccount). Ekern-Wilson [1974], Leland [1973], and Radner [1974] have used theassumption that ^ = 9jj along with spanning to prove unanimity, and referred tothis situation as ex post unanimity, to distinguish it from the case when thecontraint is not imposed, which is called ex ante unanimity.

To see more precisely the nature Of what is going on, it may be useful to considera special case. Assume a mean variance model and a risk free asset with period 2return defined as R; consider a firm whose returns are independently distributedfrom all other firms, and consider a change in its production plans which increasesthe output in all states of nature proportionately: dnj/dpj = Hj, doj/dpj^Oj where [ijand Oj are the mean and standard deviations of theyth firm's returns.

Assume that all traders have constant absolute risk aversion. Then the basicmarket valuation equation implies that there is a positive constant k such thatPj = {p.j — kaj)/R. From the first order conditions for optimality there is a positivemultiplier Af such that

(15)

The second term in brackets is the consumption effect, about which, all sharehold-ers are unanimous. However, we now show that shareholders need not be un-animous regarding the production plan because of the capital gains term. Since k isa constant relating to the risk aversions of the shareholders,

dp, kaf

Using (15) and (16) together yields dU*/dpj = \f{R9,j[{dpj/dpj)-{dyf/dpj)] +9jjkaJ). Thus, all shareholders desire to expand the firm beyond its net valuemaximizing scale, since net value maximization occurs at the p such that dp,/dp,= dyf/dp..

Note that we have used the capital asset pricing model to calculate howshareholders think a change in the risk-return of a firm will affect the price of afirm. From (16) it can be seen that shareholders do not feel that doubling theoutput of their firm in each state of nature doubles the value of the firm. If outputin each state of nature was a separate good then "perfect competition" would meanthat doubhng output in each state of nature doubles the value of the firm. If in (16)

3. Stiglitz was careful, however, to point out that this assumption of no trade was not a reasonable oneto impose except for gaining analytical insights into the problem.


we had assumed this, then dpj/dpj=pj then there would be unanimity in favor ofnet-value maximization, as can be seen from (15).

Thus, we see that when there is trade, i.e. O^j ^ 9^, there need not be unanimity.Leland ([1973], p. 16) and Radner [1974] have shown that if we assume"competitivity" then there will be unanimity. Competitivity means that eachconsumer believes that if the output of any firm increases by b% in each and everystate of nature, then the value of the firm increases by 6%. This assumption leads toimplicit prices by which all consumers can unanimously agree about the value of achange in production plan. From (10)-(15); competitivity implies unanimity withrespect to net-value maximization.

4. THE MULTIPERIOD ECONOMY

In the last section we assumed that there was only one trading period in order tosurvey the literature on unanimity. In this section we return to the model of section2 where consumers are permitted to trade in period 1. In equation (8) of section 2,we see that consumer /'s preference for a change in the yth firm's productiondecisions dp,, depends upon three terms. The first term is the period 0 wealth effect,the second term is the period 1 wealth effect, and the third term is the consumptioneffect (the fourth term is the wealth effect due to the cost of the new inputs). Wecan use the spanning assumption, (13), along with the first order conditions (5) and(6) to write (8) as

dU* dp, T dp,(t)

+ 2 \,«s(0 2 Vftw (1')

where we have used the implicit competitivity assumption that dp,^/dpj = O =dPk{O/dpj for k i= J. Note that a, does not depend upon the signal t because noneof the firms' output vectors depends upon /. In this model firms must fix theirproduction plans in period 0, no firm produces any output until period 2. Consu-mers may trade in period 1 based upon new information. From (17) it is clear thatthere will be unanimity if 9ij = 9jj = 9i,{t). However even if the Ekern-Wilson-Lelandassumption is made that ^^ = ^,. there will not, in general, be unanimity when9,i'9,j{t).

There is one situation in which there will be unanimity and that is whencompetitivity is assumed. That is, we can construct the Arrow-Debreu economy forcharacteristics as of period 1. If we can write the value of the firm in period 1 atsignal / as a melange of characteristics (i.e. an appropriate mixture of securities),for each of which there is a competitive market, then the value of the firm in eachsignal-state can be computed as in an Arrow-Debreu economy. Grossman-Stiglitz[1976a] show that with the appropriate competitivity assumption, it will always bepossible to do the above and there will be unanimity with regard to value


maximization. Thus, we showed that when the economy is an extension of anArrow-Debreu economy there will always be unanimity, even if there is trade.

As we argued in section 3, the no trade assumption was crucial to any unanimitytheorem which was not a simple extension of an Arrow-Debreu securities market.We argued in this section that new information would give rise to trade; here weargue that the life cycle of the individual will give rise to trade. (Our earlierdiscussion concerning the stages of the firm provided a third reason for trade tooccur continuously in a stock market: firms also have a life cycle.) When in-dividuals are young, they buy shares as a form of saving; when they are old theysell them, presumably to the next generation.

Assume individuals live for two periods. They work the first period, buy shares;in the second period they receive dividends—based on the firm's action in theprevious period—make decisions which will determine the dividend the periodafter, sell their shares, and finally come the proceeds. In that context, it is clear thatat the time of the decision, for the decision makers 9^ = 0. Hence all firms willmaximize their stock market value. Note, however, that if we modify the model tomake it a three period model, then there will exist shareholders in the first andthird years of their lives. For the former tf^ > 0 while for the latter, as before ^ = 0.Hence we cannot be assured that there will be unanimity unless the spanning andcompetivity assumptions are satisfied. Spanning alone is enough only if there is notrade.

5. SPANNING AND THE CHOICE OF A DEBT-EQUITY RATIO

We now return to the one trading period model of section 3. We suppose that theproduction plan y, = {y^yj) has been chosen, and the firm must now decide how tofinance v°. Let D, be the period 0 value of the debt issued by firm J. Let 1 — a bethe fraction of the firm that the initial shareholders sell to raise capital (i.e. newequity). Then yf=Dj + {\ - a)pj. Let Bj be the principal plus the interest which thefirm promises that bondholders will receive in period 2. Let by be the fraction offirm/s debt held by consumer /. Then (1) is replaced by xf{s) = '2,j9ijma.x{0,yj{s)-Bj) + '^jbymm{Bj,yj{s)). Thus, the consumer's period 2 consumption comes fromnon-defaulted debt payments and claims to residual output. Similarly (3) is re-placed by xf+j2jPj9ij + ^jD.by<'2j9ij{pj-yj'+D,)+_xf. Thus each initial share-holder owns a9ij percent of the firm which is worth a9jjPj = 9ij{pj-yj+Dj).

We assume no trade in period 1, so the consumer maximizes Uj{xf,xj,xf) subjectto the above constraints, with respect to xf, 9^, and b^,. Denote the maximized utilityby U*{Bp. Let B{Bj)^{s\yj{s)<Bj] and NB{Bj) = {s\yf{s)>Bj). We are in-terested in a change in the debt-equity ratio keeping the production plan /constant. We can calculate dUf{Bj)/dBj at B,. such <!RaXy'j{s) # B^ for all s. This isgiven by

dD,dD,—I- V

sSNB(18)

here Vj = Dj +pj, and V, t/, = Sr^.9U,{x)/dxf{t,s).The Modigliani-Miller theorem gives conditions under which a change in the


debt-equity ratio leaves the value of the firm unchanged. However, the appropriatetheorem should be that all shareholders are indifferent about the debt-equity ratio.As can be seen from (18) dVj/dBj = O is not equivalent to dUf /dBj = O. There isone important and well known situation where the two are equivalent, that is when9jj = bjj. This occurs if there is portfolio separation such that all consumers desire tohold the same mutual fund of all risky assets (e.g. when all consumers homo-geneously believe that returns on all securities are multivariate normal), i.e. hold allrisky assets in the same proportion.

We feel that the point of the Modigliani-Miller theorem is that the debt-equityratio is indeterminate because all shareholders are unanimously indifferent betweenchoices of Bj. For this to be true, it is necessary that dU*/dBj = Q, where it is welldefined. As can be seen from (18), this will not be true in general. One situation inwhich it is true is when there is no trade, i.e. 9jj = 9ij, and strong portfolioseparation, i.e. 9jj = bjj. But this will not generalize to a multiperiod model just as expost unanimity does not generalize.

It might be thought that a spanning argument will lead to unanimity in the abovecontext. It does lead to unanimity but it also implies, under weak regularityconditions, that there exist complete markets. See Grossman-Stiglitz [1976a] for aproof of this fact.

6. ON THE VALUE OF VALUE MAXIMIZATION

We have attempted to show that most of the unanimity theorems in the literatureon spanning make the assumption that there is no trade during the time betweenthe realization of firms' output and the putting of inputs in place. That is, simplespanning theorems concern firms that are not traded on the large stock exchangesof most countries. Stocks traded on these exchanges have a large trading volumeevery day because consumers get new information about the probability distribu-tion of firm output (i.e. dividends). We have shown that in such an economyconsumers will in general disagree about the production plan which their firmshould use. This disagreement arises because different stockholders anticipatedifferent capital gains and losses as new information reaches the market concerningfirm output.

A unanimity theorem could be proved in a multiperiod context if the assumptionof competitivity is made in addition to the assumption of spanning. Though thismay seem like a minor additional assumption, it leads to a very strong implicationwhich spanning above does not imply. That is, if there is spanning and competitiv-ity, then stockholders unanimously desire the firm to maximize net market value.

It is the implication of value maximization that leads us to think that the theoryis seriously incomplete. There is one class of firms where it is quite easily seen thatnet-value is not maximized. A closed end mutual fund is a firm which purchasesshares of other firms on the stock market. Its only productive decision on a givenday is to purchase or sell shares of one firm for cash or shares of other firms. Theclosed end mutual fund is itself a corporation with shares traded on the stockmarket. It is a fact that almost all closed end mutual funds sell at a substantialdiscount (see Sharpe-Sossin [1975]). That is the market value of the mutual fundsportfolio is substantially higher than the market value of the mutual fund own


shares. This means that there is a productive decision available to the manager ofthe firm which would increase its value. The manager can sell off the portfolio ofstocks for cash and then distribute the cash to the mutual fund shareholders. Asthis is not done we conclude that the shareholders of the mutual fund do not desirethe fund to maximize market value.

Most discussions of unanimity involve the choice of production decisions. Weargued that the Modigliani-Miller theorem is the result that with no bankruptcy allshareholders are unanimously indifferent among choice of the debt-equity ratio.We showed that if there is a chance of bankrupty, then shareholders need not beunanimously indifferent as to the debt-equity ratio. Since the bonds of the samematurity for different firms have different yields, there must be some chance thatfirms go bankrupt in the real world. It might be thought that the Modigliani-Millertheorem would still hold if there is spanning for bonds. However, spanning forbonds implies that there are a complete set of markets. This, of course, implies thatthe debt-equity ratio is indeterminate but it has the empirically false implicationthat firms maximize value and all risks are insurable.

7. EQUILIBRIUM IN THE CORPORATE ECONOMY

What happens when there is no unanimity, as our analysis suggests will generallybe the case? And, what happens if there is unanimity but not on the valuemaximizing strategy, as could be the case when the spanning assumption wassatisfied, but not the competitivity assumption? Wouldn't some individual takeover the firm, change its policy to the market value maximizing policy, and make apure capital gain? An answer to these questions and the formulation of a completeequilibrium theory of the market require the specification of assumptions concern-ing the information available to the shareholder concerning the take-over and theexpectations of individuals about the actions to be taken by the firm after thetake-over. We argue that there are serious problems in formulating an equilibriumtheory of take-overs. (See Grossman-Hart [1976] for a theory of the firm withoutspanning.)

Assume there is ex ante unanimity on a policy other than value maximization;assume that the individual taking over the firm announces the firm will pursue avalue maximizing strategy; individuals know that after the take-over, the individualis going to sell his shares to obtain his capital gain, and that in the newshareholders' meeting following that, all will vote for the original utility maximizingstrategy. Thus, in spite of the announcement, individuals do not expect that thefirm will pursue a value maximizing strategy, and hence the entrepreneur will notbe able to reap any capital gain. In the above example, if the take-over en-trepreneur could (because of fixed investments, say) commit the firm to the valuemaximizing strategy for one period, then, he could obtain a majority of shares atthe current market price. But unless the competitivity assumption is satisfied, thereis likely to be a downward sloping demand curve for shares of firms. The marketvalue represents the value to the marginal purchaser; to purchase a majority ofshares, even acting as a discriminating monopsonist, would be more costly than thecurrent value of the firm.

There are several other problems with arranging a successful take-over even if all


shareholders desire value maximization, but the current management is against it.(a) If the individual taking over announces it prior to his take-over, then it does notpay anybody to sell his shares; if he expects the take-over to be successful, bypostponing selling, the individual would make a capital gain. An exception is wherethe group taking over offers all shareholders exactly the maximized market value,but in this case there are no profits to be made from the take-over, (b) Anotherquandry arises if the take-over is not announced but proceeds gradually, then onlywhen the individual owns, say 10% of the shares, is the take-over bid implicitlydisclosed (as current law requires). If a successful take-over bid is associated withan increase in market value, then the market realizing this will immediately bid upthe shares upon disclosure. But then, it would pay any entrepreneur to buy 10% ofthe shares, simply to obtain a capital gain. But then, of course, disclosure will notbe a signal of a take-over bid. Take-overs have many of the informationalcharacteristics of arbitrage discussed in Grossman-Stiglitz [1976a].

We are now prepared to suggest a definition of equilibrium: consider all thepolicies with the characteristic that a majority of the shareholders who purchase theshares'* when that policy is announced, vote for the given policy against any otherpolicy. For each such policy, there is a market value. An equilibrium requires thatit be preferred by a majority and be immune from take-over. The policy with thehighest market value is the equilibrium. Clearly no other policy can be anequilibrium; for ignoring the quandaries concerning the purchase of the shares, atake-over bid which announced the given policy would be able to sustain the givenpolicy and hence a capital gain could be made. If individuals assume that onlypolicies to be eventually pursued by the firm—and hence the policies which arerelevant—are those which can be sustained in the above sense, the market priceassociated with any other policy must be lower than that market price, and hencethere will be no take-over attempts against it.

8. CONCLUDING REMARKS

This paper has argued that (a) spanning does not imply shareholder unanimity forcorporations that are traded, (b) If there is unanimity for a traded firm due to theassumption of competitivity, then firms must maximize value, (c) But closed endfunds do not maximize value, and these companies are the ones we would mostexpect to do so. We thus find spanning an unsatisfactory assumption, (d) Wefurther argue that there are fundamental difficulties with justifying value maximiza-tion on the basis of take-over bids when firms are undervalued.

REFERENCES

P. A. Diamond. [1967], "The Role of a Stock Market in a General Equilibrium Model with Technologi-cal Uncertainty," American Economic Review, 57, 759-776.

S. Ekern and R. Wilson. [1974], "On the Theory of the Firm in an Economy with Incomplete Markets,"The Betl Journal of Economics and Management Science, Vol. 5, No. 1, 171-180.

4. Clearly, as in any voting model, there may not exist an equilibrium in the stockmarket votingmodel; it seems there are large costs associated with changing plans and with indecisiveness, andaccordingly we suggest the following modification: a majority voting equilibrium is a proposal whichcannot be defeated by any proposal which cannot be defeated by some other proposal.


S. Grossman and J. Stiglitz. [1976a], "On Stockholder Unanimity in Making Production and FinancialDecisions," Technical Report No. 250, Economics Series, Institute for Mathematical Studies inthe Social Sciences (IMSSS), Stanford University.and . [1976b], "Information and Competitive Price Systems," American Economic Review,

Vol. 66, No. 2, pp. 246-253.and O. Hart [1976], "A Theory of Competitive Equilibrium in Stock Market Economies,"

Technical Report No. 230, Economics Series, IMSSS, Stanford University.H. Leland. [1973], "Capital Asset Markets, Production and Optimality: A Synthesis," Technical Report

No. 115, Economics Series, IMSSS, Stanford University.. [1974], "Production Theory and the Stock Market," The Bett Journal of Economics andManagement Science, Vol. 5, No. 1, 125-144.

R. Radner. [1974], "A Note on Unanimity of Stockholders' Preferences Among Alternative ProductionPlans: A Reformulation of the Ekern-Wilson Model," The Belt Journal of Economics andManagement Science, Vol. 5, No. 1, 181-186.

W. F. Sharpe and H. B. Sossin. [1975], "Closed-End Investment Companies in the United States: Riskand Return," in European Finance Association, 1974 Proceedings (B. Jacquillant, editor). NorthHolland, 37-63.

J. E. Stiglitz. [1970], "On the Optimality of the Stock Market Allocation of Investment," paper presentedat the Far Eastern Meetings of the Econometric Society, Tokyo, June 27-29, 1970.. [1972], "Some Aspects of the Pure Theory of Corporate Finance: Bankruptcies and Take-Overs," The Bell Journat of Economics and Management Science, Vol. 3, No. 2, Autumn 1972,458-482.

on value maximization and alternative objectives of the firm

Documents